Properties

Label 891.2.n.e.190.2
Level $891$
Weight $2$
Character 891.190
Analytic conductor $7.115$
Analytic rank $0$
Dimension $16$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(136,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([20, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.n (of order \(15\), degree \(8\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{14} - 15x^{12} + 116x^{10} + 69x^{8} - 814x^{6} + 2420x^{4} - 7986x^{2} + 14641 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 190.2
Root \(1.96317 + 0.874061i\) of defining polynomial
Character \(\chi\) \(=\) 891.190
Dual form 891.2.n.e.136.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.96317 + 0.874061i) q^{2} +(1.75181 + 1.94558i) q^{4} +(-1.96317 + 0.874061i) q^{5} +(4.14350 - 0.880728i) q^{7} +(0.410415 + 1.26313i) q^{8} -4.61803 q^{10} +(2.28779 + 2.40125i) q^{11} +(-0.0246758 - 0.234775i) q^{13} +(8.90422 + 1.89265i) q^{14} +(0.248983 - 2.36892i) q^{16} +(4.96199 + 3.60510i) q^{17} +(-0.736068 - 2.26538i) q^{19} +(-5.13966 - 2.28832i) q^{20} +(2.39248 + 6.71375i) q^{22} +(-1.99220 + 3.45059i) q^{23} +(-0.255585 + 0.283856i) q^{25} +(0.156765 - 0.482472i) q^{26} +(8.97214 + 6.51864i) q^{28} +(-6.80222 + 1.44586i) q^{29} +(0.482716 + 4.59274i) q^{31} +(3.88751 - 6.73336i) q^{32} +(6.59017 + 11.4145i) q^{34} +(-7.36460 + 5.35069i) q^{35} +(0.545085 - 1.67760i) q^{37} +(0.535055 - 5.09071i) q^{38} +(-1.90977 - 2.12101i) q^{40} +(2.90489 + 0.617454i) q^{41} +(-1.35410 - 2.34537i) q^{43} +(-0.664066 + 8.65761i) q^{44} +(-6.92705 + 5.03280i) q^{46} +(2.32663 - 2.58398i) q^{47} +(9.99809 - 4.45144i) q^{49} +(-0.749866 + 0.333862i) q^{50} +(0.413545 - 0.459289i) q^{52} +(1.48490 - 1.07884i) q^{53} +(-6.59017 - 2.71441i) q^{55} +(2.81303 + 4.87231i) q^{56} +(-14.6177 - 3.10709i) q^{58} +(-4.99271 - 5.54496i) q^{59} +(1.18391 - 11.2642i) q^{61} +(-3.06668 + 9.43826i) q^{62} +(9.66312 - 7.02067i) q^{64} +(0.253650 + 0.439335i) q^{65} +(1.42705 - 2.47172i) q^{67} +(1.67845 + 15.9694i) q^{68} +(-19.1348 + 4.06723i) q^{70} +(-8.69273 - 6.31564i) q^{71} +(0.763932 - 2.35114i) q^{73} +(2.53642 - 2.81698i) q^{74} +(3.11803 - 5.40059i) q^{76} +(11.5943 + 7.93468i) q^{77} +(-8.65323 - 3.85266i) q^{79} +(1.58178 + 4.86822i) q^{80} +(5.16312 + 3.75123i) q^{82} +(-0.865738 + 8.23694i) q^{83} +(-12.8923 - 2.74035i) q^{85} +(-0.608337 - 5.78794i) q^{86} +(-2.09415 + 3.87528i) q^{88} +8.90937 q^{89} +(-0.309017 - 0.951057i) q^{91} +(-10.2033 + 2.16878i) q^{92} +(6.82614 - 3.03919i) q^{94} +(3.42511 + 3.80397i) q^{95} +(10.7784 + 4.79883i) q^{97} +23.5188 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{4} + 6 q^{7} - 56 q^{10} + 6 q^{13} - 2 q^{16} + 24 q^{19} - 28 q^{22} - 8 q^{25} + 72 q^{28} - 12 q^{31} + 16 q^{34} - 36 q^{37} + 16 q^{40} + 32 q^{43} - 84 q^{46} + 44 q^{49} - 6 q^{52} - 16 q^{55}+ \cdots + 54 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.96317 + 0.874061i 1.38817 + 0.618055i 0.958542 0.284950i \(-0.0919770\pi\)
0.429631 + 0.903005i \(0.358644\pi\)
\(3\) 0 0
\(4\) 1.75181 + 1.94558i 0.875903 + 0.972789i
\(5\) −1.96317 + 0.874061i −0.877958 + 0.390892i −0.795680 0.605717i \(-0.792886\pi\)
−0.0822781 + 0.996609i \(0.526220\pi\)
\(6\) 0 0
\(7\) 4.14350 0.880728i 1.56610 0.332884i 0.658451 0.752623i \(-0.271212\pi\)
0.907645 + 0.419740i \(0.137879\pi\)
\(8\) 0.410415 + 1.26313i 0.145104 + 0.446583i
\(9\) 0 0
\(10\) −4.61803 −1.46035
\(11\) 2.28779 + 2.40125i 0.689794 + 0.724005i
\(12\) 0 0
\(13\) −0.0246758 0.234775i −0.00684384 0.0651148i 0.990567 0.137030i \(-0.0437556\pi\)
−0.997411 + 0.0719150i \(0.977089\pi\)
\(14\) 8.90422 + 1.89265i 2.37975 + 0.505832i
\(15\) 0 0
\(16\) 0.248983 2.36892i 0.0622458 0.592229i
\(17\) 4.96199 + 3.60510i 1.20346 + 0.874364i 0.994620 0.103586i \(-0.0330318\pi\)
0.208838 + 0.977950i \(0.433032\pi\)
\(18\) 0 0
\(19\) −0.736068 2.26538i −0.168866 0.519715i 0.830435 0.557116i \(-0.188092\pi\)
−0.999300 + 0.0374011i \(0.988092\pi\)
\(20\) −5.13966 2.28832i −1.14926 0.511684i
\(21\) 0 0
\(22\) 2.39248 + 6.71375i 0.510079 + 1.43138i
\(23\) −1.99220 + 3.45059i −0.415402 + 0.719497i −0.995471 0.0950706i \(-0.969692\pi\)
0.580069 + 0.814567i \(0.303026\pi\)
\(24\) 0 0
\(25\) −0.255585 + 0.283856i −0.0511170 + 0.0567712i
\(26\) 0.156765 0.482472i 0.0307441 0.0946205i
\(27\) 0 0
\(28\) 8.97214 + 6.51864i 1.69557 + 1.23191i
\(29\) −6.80222 + 1.44586i −1.26314 + 0.268489i −0.790333 0.612677i \(-0.790093\pi\)
−0.472807 + 0.881166i \(0.656759\pi\)
\(30\) 0 0
\(31\) 0.482716 + 4.59274i 0.0866984 + 0.824880i 0.948317 + 0.317324i \(0.102784\pi\)
−0.861619 + 0.507556i \(0.830549\pi\)
\(32\) 3.88751 6.73336i 0.687221 1.19030i
\(33\) 0 0
\(34\) 6.59017 + 11.4145i 1.13020 + 1.95757i
\(35\) −7.36460 + 5.35069i −1.24484 + 0.904432i
\(36\) 0 0
\(37\) 0.545085 1.67760i 0.0896114 0.275796i −0.896201 0.443649i \(-0.853684\pi\)
0.985812 + 0.167854i \(0.0536836\pi\)
\(38\) 0.535055 5.09071i 0.0867974 0.825822i
\(39\) 0 0
\(40\) −1.90977 2.12101i −0.301961 0.335361i
\(41\) 2.90489 + 0.617454i 0.453668 + 0.0964302i 0.429078 0.903267i \(-0.358839\pi\)
0.0245903 + 0.999698i \(0.492172\pi\)
\(42\) 0 0
\(43\) −1.35410 2.34537i −0.206499 0.357666i 0.744111 0.668056i \(-0.232874\pi\)
−0.950609 + 0.310390i \(0.899540\pi\)
\(44\) −0.664066 + 8.65761i −0.100112 + 1.30518i
\(45\) 0 0
\(46\) −6.92705 + 5.03280i −1.02134 + 0.742045i
\(47\) 2.32663 2.58398i 0.339374 0.376913i −0.549165 0.835714i \(-0.685054\pi\)
0.888539 + 0.458801i \(0.151721\pi\)
\(48\) 0 0
\(49\) 9.99809 4.45144i 1.42830 0.635919i
\(50\) −0.749866 + 0.333862i −0.106047 + 0.0472152i
\(51\) 0 0
\(52\) 0.413545 0.459289i 0.0573484 0.0636919i
\(53\) 1.48490 1.07884i 0.203966 0.148190i −0.481113 0.876658i \(-0.659767\pi\)
0.685079 + 0.728468i \(0.259767\pi\)
\(54\) 0 0
\(55\) −6.59017 2.71441i −0.888618 0.366011i
\(56\) 2.81303 + 4.87231i 0.375906 + 0.651089i
\(57\) 0 0
\(58\) −14.6177 3.10709i −1.91940 0.407981i
\(59\) −4.99271 5.54496i −0.649995 0.721893i 0.324604 0.945850i \(-0.394769\pi\)
−0.974599 + 0.223957i \(0.928102\pi\)
\(60\) 0 0
\(61\) 1.18391 11.2642i 0.151585 1.44223i −0.609091 0.793100i \(-0.708466\pi\)
0.760676 0.649132i \(-0.224868\pi\)
\(62\) −3.06668 + 9.43826i −0.389468 + 1.19866i
\(63\) 0 0
\(64\) 9.66312 7.02067i 1.20789 0.877583i
\(65\) 0.253650 + 0.439335i 0.0314615 + 0.0544929i
\(66\) 0 0
\(67\) 1.42705 2.47172i 0.174342 0.301969i −0.765591 0.643327i \(-0.777553\pi\)
0.939933 + 0.341358i \(0.110887\pi\)
\(68\) 1.67845 + 15.9694i 0.203542 + 1.93657i
\(69\) 0 0
\(70\) −19.1348 + 4.06723i −2.28705 + 0.486127i
\(71\) −8.69273 6.31564i −1.03164 0.749528i −0.0630016 0.998013i \(-0.520067\pi\)
−0.968636 + 0.248485i \(0.920067\pi\)
\(72\) 0 0
\(73\) 0.763932 2.35114i 0.0894115 0.275180i −0.896346 0.443356i \(-0.853788\pi\)
0.985757 + 0.168176i \(0.0537877\pi\)
\(74\) 2.53642 2.81698i 0.294853 0.327467i
\(75\) 0 0
\(76\) 3.11803 5.40059i 0.357663 0.619491i
\(77\) 11.5943 + 7.93468i 1.32129 + 0.904240i
\(78\) 0 0
\(79\) −8.65323 3.85266i −0.973564 0.433459i −0.142597 0.989781i \(-0.545545\pi\)
−0.830967 + 0.556322i \(0.812212\pi\)
\(80\) 1.58178 + 4.86822i 0.176849 + 0.544284i
\(81\) 0 0
\(82\) 5.16312 + 3.75123i 0.570171 + 0.414254i
\(83\) −0.865738 + 8.23694i −0.0950271 + 0.904122i 0.838328 + 0.545167i \(0.183534\pi\)
−0.933355 + 0.358955i \(0.883133\pi\)
\(84\) 0 0
\(85\) −12.8923 2.74035i −1.39837 0.297232i
\(86\) −0.608337 5.78794i −0.0655987 0.624130i
\(87\) 0 0
\(88\) −2.09415 + 3.87528i −0.223237 + 0.413106i
\(89\) 8.90937 0.944392 0.472196 0.881494i \(-0.343462\pi\)
0.472196 + 0.881494i \(0.343462\pi\)
\(90\) 0 0
\(91\) −0.309017 0.951057i −0.0323938 0.0996978i
\(92\) −10.2033 + 2.16878i −1.06377 + 0.226111i
\(93\) 0 0
\(94\) 6.82614 3.03919i 0.704062 0.313469i
\(95\) 3.42511 + 3.80397i 0.351409 + 0.390280i
\(96\) 0 0
\(97\) 10.7784 + 4.79883i 1.09438 + 0.487247i 0.872890 0.487916i \(-0.162243\pi\)
0.221485 + 0.975164i \(0.428910\pi\)
\(98\) 23.5188 2.37576
\(99\) 0 0
\(100\) −1.00000 −0.100000
\(101\) −0.286423 0.127524i −0.0285002 0.0126891i 0.392437 0.919779i \(-0.371632\pi\)
−0.420937 + 0.907090i \(0.638299\pi\)
\(102\) 0 0
\(103\) −7.32315 8.13318i −0.721571 0.801386i 0.265081 0.964226i \(-0.414601\pi\)
−0.986652 + 0.162840i \(0.947935\pi\)
\(104\) 0.286423 0.127524i 0.0280861 0.0125047i
\(105\) 0 0
\(106\) 3.85808 0.820060i 0.374730 0.0796513i
\(107\) −3.38021 10.4032i −0.326777 1.00572i −0.970632 0.240569i \(-0.922666\pi\)
0.643855 0.765147i \(-0.277334\pi\)
\(108\) 0 0
\(109\) −13.7082 −1.31301 −0.656504 0.754323i \(-0.727965\pi\)
−0.656504 + 0.754323i \(0.727965\pi\)
\(110\) −10.5651 11.0891i −1.00734 1.05730i
\(111\) 0 0
\(112\) −1.05471 10.0349i −0.0996607 0.948208i
\(113\) −17.5018 3.72011i −1.64643 0.349959i −0.710922 0.703271i \(-0.751722\pi\)
−0.935505 + 0.353312i \(0.885055\pi\)
\(114\) 0 0
\(115\) 0.895005 8.51540i 0.0834596 0.794065i
\(116\) −14.7292 10.7014i −1.36757 0.993599i
\(117\) 0 0
\(118\) −4.95492 15.2497i −0.456137 1.40385i
\(119\) 23.7351 + 10.5675i 2.17579 + 0.968726i
\(120\) 0 0
\(121\) −0.532046 + 10.9871i −0.0483678 + 0.998830i
\(122\) 12.1698 21.0788i 1.10180 1.90838i
\(123\) 0 0
\(124\) −8.08990 + 8.98475i −0.726495 + 0.806854i
\(125\) 3.57398 10.9996i 0.319666 0.983832i
\(126\) 0 0
\(127\) 2.23607 + 1.62460i 0.198419 + 0.144160i 0.682558 0.730831i \(-0.260867\pi\)
−0.484139 + 0.874991i \(0.660867\pi\)
\(128\) 9.89665 2.10360i 0.874749 0.185934i
\(129\) 0 0
\(130\) 0.113954 + 1.08420i 0.00999441 + 0.0950904i
\(131\) −1.23125 + 2.13258i −0.107574 + 0.186324i −0.914787 0.403936i \(-0.867642\pi\)
0.807213 + 0.590261i \(0.200975\pi\)
\(132\) 0 0
\(133\) −5.04508 8.73834i −0.437464 0.757710i
\(134\) 4.96199 3.60510i 0.428650 0.311433i
\(135\) 0 0
\(136\) −2.51722 + 7.74721i −0.215850 + 0.664318i
\(137\) −0.0327727 + 0.311812i −0.00279996 + 0.0266399i −0.995833 0.0911992i \(-0.970930\pi\)
0.993033 + 0.117839i \(0.0375967\pi\)
\(138\) 0 0
\(139\) −7.61602 8.45845i −0.645983 0.717436i 0.327843 0.944732i \(-0.393678\pi\)
−0.973826 + 0.227296i \(0.927012\pi\)
\(140\) −23.3116 4.95502i −1.97019 0.418776i
\(141\) 0 0
\(142\) −11.5451 19.9967i −0.968842 1.67808i
\(143\) 0.507301 0.596368i 0.0424226 0.0498708i
\(144\) 0 0
\(145\) 12.0902 8.78402i 1.00403 0.729473i
\(146\) 3.55477 3.94797i 0.294195 0.326737i
\(147\) 0 0
\(148\) 4.21878 1.87832i 0.346782 0.154397i
\(149\) −4.21277 + 1.87565i −0.345124 + 0.153659i −0.571976 0.820270i \(-0.693823\pi\)
0.226853 + 0.973929i \(0.427156\pi\)
\(150\) 0 0
\(151\) −8.85666 + 9.83632i −0.720745 + 0.800468i −0.986533 0.163563i \(-0.947701\pi\)
0.265788 + 0.964031i \(0.414368\pi\)
\(152\) 2.55938 1.85950i 0.207593 0.150825i
\(153\) 0 0
\(154\) 15.8262 + 25.7113i 1.27531 + 2.07187i
\(155\) −4.96199 8.59441i −0.398556 0.690320i
\(156\) 0 0
\(157\) 20.2012 + 4.29389i 1.61223 + 0.342690i 0.923878 0.382688i \(-0.125002\pi\)
0.688351 + 0.725378i \(0.258335\pi\)
\(158\) −13.6203 15.1269i −1.08357 1.20343i
\(159\) 0 0
\(160\) −1.74648 + 16.6167i −0.138072 + 1.31366i
\(161\) −5.21564 + 16.0521i −0.411050 + 1.26508i
\(162\) 0 0
\(163\) −1.11803 + 0.812299i −0.0875712 + 0.0636242i −0.630709 0.776019i \(-0.717236\pi\)
0.543138 + 0.839643i \(0.317236\pi\)
\(164\) 3.88751 + 6.73336i 0.303563 + 0.525787i
\(165\) 0 0
\(166\) −8.89919 + 15.4138i −0.690711 + 1.19635i
\(167\) 1.12314 + 10.6859i 0.0869110 + 0.826903i 0.947962 + 0.318384i \(0.103140\pi\)
−0.861051 + 0.508519i \(0.830193\pi\)
\(168\) 0 0
\(169\) 12.6614 2.69127i 0.973955 0.207020i
\(170\) −22.9146 16.6485i −1.75747 1.27688i
\(171\) 0 0
\(172\) 2.19098 6.74315i 0.167061 0.514161i
\(173\) −8.96706 + 9.95893i −0.681753 + 0.757164i −0.980361 0.197212i \(-0.936811\pi\)
0.298608 + 0.954376i \(0.403478\pi\)
\(174\) 0 0
\(175\) −0.809017 + 1.40126i −0.0611559 + 0.105925i
\(176\) 6.25799 4.82171i 0.471714 0.363450i
\(177\) 0 0
\(178\) 17.4906 + 7.78734i 1.31098 + 0.583686i
\(179\) 0.604187 + 1.85950i 0.0451590 + 0.138985i 0.971094 0.238698i \(-0.0767207\pi\)
−0.925935 + 0.377684i \(0.876721\pi\)
\(180\) 0 0
\(181\) −9.89919 7.19218i −0.735801 0.534591i 0.155592 0.987821i \(-0.450271\pi\)
−0.891393 + 0.453231i \(0.850271\pi\)
\(182\) 0.224628 2.13719i 0.0166505 0.158419i
\(183\) 0 0
\(184\) −5.17616 1.10023i −0.381591 0.0811098i
\(185\) 0.396228 + 3.76986i 0.0291312 + 0.277165i
\(186\) 0 0
\(187\) 2.69523 + 20.1627i 0.197095 + 1.47444i
\(188\) 9.10315 0.663915
\(189\) 0 0
\(190\) 3.39919 + 10.4616i 0.246603 + 0.758966i
\(191\) 9.70711 2.06331i 0.702382 0.149296i 0.157142 0.987576i \(-0.449772\pi\)
0.545240 + 0.838280i \(0.316439\pi\)
\(192\) 0 0
\(193\) 6.74376 3.00252i 0.485427 0.216126i −0.149405 0.988776i \(-0.547736\pi\)
0.634832 + 0.772650i \(0.281069\pi\)
\(194\) 16.9653 + 18.8419i 1.21804 + 1.35277i
\(195\) 0 0
\(196\) 26.1753 + 11.6540i 1.86967 + 0.832429i
\(197\) −2.46249 −0.175445 −0.0877226 0.996145i \(-0.527959\pi\)
−0.0877226 + 0.996145i \(0.527959\pi\)
\(198\) 0 0
\(199\) 0.416408 0.0295184 0.0147592 0.999891i \(-0.495302\pi\)
0.0147592 + 0.999891i \(0.495302\pi\)
\(200\) −0.463442 0.206338i −0.0327703 0.0145903i
\(201\) 0 0
\(202\) −0.450835 0.500703i −0.0317206 0.0352293i
\(203\) −26.9116 + 11.9818i −1.88882 + 0.840958i
\(204\) 0 0
\(205\) −6.24250 + 1.32689i −0.435995 + 0.0926737i
\(206\) −7.26771 22.3677i −0.506366 1.55843i
\(207\) 0 0
\(208\) −0.562306 −0.0389889
\(209\) 3.75580 6.95021i 0.259794 0.480756i
\(210\) 0 0
\(211\) 1.88511 + 17.9356i 0.129776 + 1.23474i 0.844585 + 0.535421i \(0.179847\pi\)
−0.714809 + 0.699320i \(0.753486\pi\)
\(212\) 4.70022 + 0.999062i 0.322812 + 0.0686159i
\(213\) 0 0
\(214\) 2.45711 23.3778i 0.167964 1.59807i
\(215\) 4.70834 + 3.42081i 0.321106 + 0.233297i
\(216\) 0 0
\(217\) 6.04508 + 18.6049i 0.410367 + 1.26298i
\(218\) −26.9116 11.9818i −1.82268 0.811511i
\(219\) 0 0
\(220\) −6.26360 17.5768i −0.422292 1.18503i
\(221\) 0.723944 1.25391i 0.0486978 0.0843470i
\(222\) 0 0
\(223\) 2.12806 2.36345i 0.142506 0.158269i −0.667667 0.744460i \(-0.732707\pi\)
0.810172 + 0.586192i \(0.199374\pi\)
\(224\) 10.1776 31.3235i 0.680021 2.09289i
\(225\) 0 0
\(226\) −31.1074 22.6008i −2.06923 1.50339i
\(227\) −10.6995 + 2.27426i −0.710154 + 0.150948i −0.548806 0.835950i \(-0.684917\pi\)
−0.161348 + 0.986898i \(0.551584\pi\)
\(228\) 0 0
\(229\) 1.93086 + 18.3709i 0.127595 + 1.21399i 0.851600 + 0.524192i \(0.175632\pi\)
−0.724005 + 0.689794i \(0.757701\pi\)
\(230\) 9.20003 15.9349i 0.606632 1.05072i
\(231\) 0 0
\(232\) −4.61803 7.99867i −0.303189 0.525138i
\(233\) −18.6167 + 13.5258i −1.21962 + 0.886106i −0.996069 0.0885854i \(-0.971765\pi\)
−0.223552 + 0.974692i \(0.571765\pi\)
\(234\) 0 0
\(235\) −2.30902 + 7.10642i −0.150624 + 0.463572i
\(236\) 2.04190 19.4274i 0.132917 1.26462i
\(237\) 0 0
\(238\) 37.3594 + 41.4919i 2.42165 + 2.68952i
\(239\) −11.1958 2.37973i −0.724193 0.153932i −0.168956 0.985624i \(-0.554039\pi\)
−0.555238 + 0.831692i \(0.687373\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) −10.6479 + 21.1046i −0.684474 + 1.35665i
\(243\) 0 0
\(244\) 23.9894 17.4293i 1.53576 1.11580i
\(245\) −15.7372 + 17.4779i −1.00541 + 1.11662i
\(246\) 0 0
\(247\) −0.513692 + 0.228710i −0.0326854 + 0.0145525i
\(248\) −5.60310 + 2.49466i −0.355797 + 0.158411i
\(249\) 0 0
\(250\) 16.6306 18.4702i 1.05181 1.16816i
\(251\) 18.3631 13.3415i 1.15907 0.842111i 0.169406 0.985546i \(-0.445815\pi\)
0.989660 + 0.143436i \(0.0458150\pi\)
\(252\) 0 0
\(253\) −12.8435 + 3.11044i −0.807461 + 0.195552i
\(254\) 2.96979 + 5.14383i 0.186341 + 0.322753i
\(255\) 0 0
\(256\) −2.09901 0.446157i −0.131188 0.0278848i
\(257\) −8.28816 9.20494i −0.517001 0.574188i 0.426949 0.904276i \(-0.359588\pi\)
−0.943950 + 0.330087i \(0.892922\pi\)
\(258\) 0 0
\(259\) 0.781051 7.43120i 0.0485321 0.461752i
\(260\) −0.410415 + 1.26313i −0.0254529 + 0.0783359i
\(261\) 0 0
\(262\) −4.28115 + 3.11044i −0.264491 + 0.192164i
\(263\) 3.22344 + 5.58316i 0.198766 + 0.344273i 0.948129 0.317887i \(-0.102973\pi\)
−0.749363 + 0.662160i \(0.769640\pi\)
\(264\) 0 0
\(265\) −1.97214 + 3.41584i −0.121147 + 0.209833i
\(266\) −2.26653 21.5646i −0.138970 1.32221i
\(267\) 0 0
\(268\) 7.30885 1.55354i 0.446459 0.0948978i
\(269\) −16.3709 11.8941i −0.998149 0.725198i −0.0364584 0.999335i \(-0.511608\pi\)
−0.961690 + 0.274138i \(0.911608\pi\)
\(270\) 0 0
\(271\) −0.298374 + 0.918300i −0.0181249 + 0.0557828i −0.959710 0.280993i \(-0.909336\pi\)
0.941585 + 0.336775i \(0.109336\pi\)
\(272\) 9.77562 10.8569i 0.592734 0.658298i
\(273\) 0 0
\(274\) −0.336881 + 0.583495i −0.0203517 + 0.0352502i
\(275\) −1.26634 + 0.0356777i −0.0763629 + 0.00215145i
\(276\) 0 0
\(277\) 17.7063 + 7.88336i 1.06387 + 0.473665i 0.862608 0.505873i \(-0.168829\pi\)
0.201261 + 0.979538i \(0.435496\pi\)
\(278\) −7.55837 23.2623i −0.453321 1.39518i
\(279\) 0 0
\(280\) −9.78115 7.10642i −0.584536 0.424690i
\(281\) 1.73148 16.4739i 0.103291 0.982750i −0.813007 0.582254i \(-0.802171\pi\)
0.916298 0.400496i \(-0.131162\pi\)
\(282\) 0 0
\(283\) 10.7051 + 2.27544i 0.636353 + 0.135261i 0.514781 0.857322i \(-0.327873\pi\)
0.121572 + 0.992583i \(0.461207\pi\)
\(284\) −2.94041 27.9762i −0.174481 1.66008i
\(285\) 0 0
\(286\) 1.51718 0.727362i 0.0897128 0.0430098i
\(287\) 12.5802 0.742588
\(288\) 0 0
\(289\) 6.37132 + 19.6089i 0.374784 + 1.15347i
\(290\) 31.4129 6.67701i 1.84463 0.392088i
\(291\) 0 0
\(292\) 5.91259 2.63245i 0.346008 0.154053i
\(293\) −3.34498 3.71498i −0.195416 0.217031i 0.637471 0.770474i \(-0.279980\pi\)
−0.832887 + 0.553443i \(0.813314\pi\)
\(294\) 0 0
\(295\) 14.6482 + 6.52180i 0.852851 + 0.379714i
\(296\) 2.34273 0.136169
\(297\) 0 0
\(298\) −9.90983 −0.574061
\(299\) 0.859270 + 0.382571i 0.0496928 + 0.0221247i
\(300\) 0 0
\(301\) −7.67636 8.52546i −0.442458 0.491399i
\(302\) −25.9847 + 11.5691i −1.49525 + 0.665729i
\(303\) 0 0
\(304\) −5.54978 + 1.17964i −0.318302 + 0.0676571i
\(305\) 7.52136 + 23.1484i 0.430672 + 1.32547i
\(306\) 0 0
\(307\) 17.2705 0.985680 0.492840 0.870120i \(-0.335959\pi\)
0.492840 + 0.870120i \(0.335959\pi\)
\(308\) 4.87344 + 36.4576i 0.277690 + 2.07737i
\(309\) 0 0
\(310\) −2.22920 21.2094i −0.126610 1.20461i
\(311\) 28.1289 + 5.97898i 1.59504 + 0.339037i 0.917900 0.396813i \(-0.129884\pi\)
0.677145 + 0.735850i \(0.263217\pi\)
\(312\) 0 0
\(313\) −3.30858 + 31.4791i −0.187012 + 1.77930i 0.351010 + 0.936372i \(0.385838\pi\)
−0.538022 + 0.842931i \(0.680828\pi\)
\(314\) 35.9053 + 26.0867i 2.02625 + 1.47216i
\(315\) 0 0
\(316\) −7.66312 23.5847i −0.431084 1.32674i
\(317\) −0.286423 0.127524i −0.0160871 0.00716245i 0.398677 0.917091i \(-0.369469\pi\)
−0.414764 + 0.909929i \(0.636136\pi\)
\(318\) 0 0
\(319\) −19.0339 13.0260i −1.06569 0.729318i
\(320\) −12.8339 + 22.2289i −0.717436 + 1.24264i
\(321\) 0 0
\(322\) −24.2697 + 26.9542i −1.35250 + 1.50210i
\(323\) 4.51457 13.8944i 0.251197 0.773105i
\(324\) 0 0
\(325\) 0.0729490 + 0.0530006i 0.00404648 + 0.00293994i
\(326\) −2.90489 + 0.617454i −0.160887 + 0.0341976i
\(327\) 0 0
\(328\) 0.412289 + 3.92266i 0.0227648 + 0.216593i
\(329\) 7.36460 12.7559i 0.406024 0.703253i
\(330\) 0 0
\(331\) −3.64590 6.31488i −0.200397 0.347097i 0.748260 0.663406i \(-0.230890\pi\)
−0.948656 + 0.316309i \(0.897556\pi\)
\(332\) −17.5422 + 12.7452i −0.962755 + 0.699482i
\(333\) 0 0
\(334\) −7.13525 + 21.9601i −0.390424 + 1.20160i
\(335\) −0.641110 + 6.09976i −0.0350276 + 0.333265i
\(336\) 0 0
\(337\) −17.8340 19.8066i −0.971479 1.07894i −0.996854 0.0792589i \(-0.974745\pi\)
0.0253749 0.999678i \(-0.491922\pi\)
\(338\) 27.2089 + 5.78342i 1.47997 + 0.314577i
\(339\) 0 0
\(340\) −17.2533 29.8836i −0.935691 1.62066i
\(341\) −9.92398 + 11.6663i −0.537413 + 0.631767i
\(342\) 0 0
\(343\) 13.5172 9.82084i 0.729861 0.530275i
\(344\) 2.40676 2.67298i 0.129764 0.144117i
\(345\) 0 0
\(346\) −26.3086 + 11.7134i −1.41436 + 0.629714i
\(347\) 22.9852 10.2337i 1.23391 0.549373i 0.316986 0.948430i \(-0.397329\pi\)
0.916926 + 0.399057i \(0.130662\pi\)
\(348\) 0 0
\(349\) 6.14285 6.82232i 0.328819 0.365191i −0.555954 0.831213i \(-0.687647\pi\)
0.884773 + 0.466023i \(0.154314\pi\)
\(350\) −2.81303 + 2.04378i −0.150363 + 0.109245i
\(351\) 0 0
\(352\) 25.0623 6.06961i 1.33583 0.323511i
\(353\) 16.8782 + 29.2338i 0.898334 + 1.55596i 0.829624 + 0.558323i \(0.188555\pi\)
0.0687102 + 0.997637i \(0.478112\pi\)
\(354\) 0 0
\(355\) 22.5856 + 4.80072i 1.19872 + 0.254796i
\(356\) 15.6075 + 17.3339i 0.827196 + 0.918694i
\(357\) 0 0
\(358\) −0.439190 + 4.17861i −0.0232119 + 0.220846i
\(359\) 0.627058 1.92989i 0.0330949 0.101856i −0.933145 0.359501i \(-0.882947\pi\)
0.966239 + 0.257646i \(0.0829468\pi\)
\(360\) 0 0
\(361\) 10.7812 7.83297i 0.567429 0.412261i
\(362\) −13.1474 22.7720i −0.691013 1.19687i
\(363\) 0 0
\(364\) 1.30902 2.26728i 0.0686111 0.118838i
\(365\) 0.555310 + 5.28342i 0.0290663 + 0.276547i
\(366\) 0 0
\(367\) −22.5311 + 4.78913i −1.17611 + 0.249991i −0.754199 0.656645i \(-0.771975\pi\)
−0.421914 + 0.906636i \(0.638641\pi\)
\(368\) 7.67813 + 5.57849i 0.400250 + 0.290799i
\(369\) 0 0
\(370\) −2.51722 + 7.74721i −0.130864 + 0.402758i
\(371\) 5.20250 5.77796i 0.270100 0.299977i
\(372\) 0 0
\(373\) 7.20820 12.4850i 0.373227 0.646448i −0.616833 0.787094i \(-0.711585\pi\)
0.990060 + 0.140646i \(0.0449180\pi\)
\(374\) −12.3322 + 41.9387i −0.637684 + 2.16860i
\(375\) 0 0
\(376\) 4.21878 + 1.87832i 0.217567 + 0.0968671i
\(377\) 0.507301 + 1.56131i 0.0261273 + 0.0804116i
\(378\) 0 0
\(379\) −5.04508 3.66547i −0.259149 0.188282i 0.450623 0.892714i \(-0.351202\pi\)
−0.709772 + 0.704432i \(0.751202\pi\)
\(380\) −1.40079 + 13.3277i −0.0718592 + 0.683694i
\(381\) 0 0
\(382\) 20.8602 + 4.43397i 1.06730 + 0.226862i
\(383\) 3.56127 + 33.8832i 0.181972 + 1.73135i 0.580557 + 0.814220i \(0.302835\pi\)
−0.398585 + 0.917132i \(0.630498\pi\)
\(384\) 0 0
\(385\) −29.6970 5.44302i −1.51350 0.277402i
\(386\) 15.8636 0.807434
\(387\) 0 0
\(388\) 9.54508 + 29.3768i 0.484578 + 1.49138i
\(389\) −21.8229 + 4.63860i −1.10647 + 0.235186i −0.724694 0.689071i \(-0.758019\pi\)
−0.381771 + 0.924257i \(0.624686\pi\)
\(390\) 0 0
\(391\) −22.3249 + 9.93971i −1.12902 + 0.502673i
\(392\) 9.72610 + 10.8019i 0.491242 + 0.545580i
\(393\) 0 0
\(394\) −4.83430 2.15237i −0.243548 0.108435i
\(395\) 20.3553 1.02418
\(396\) 0 0
\(397\) 24.4164 1.22542 0.612712 0.790306i \(-0.290078\pi\)
0.612712 + 0.790306i \(0.290078\pi\)
\(398\) 0.817481 + 0.363966i 0.0409766 + 0.0182440i
\(399\) 0 0
\(400\) 0.608795 + 0.676135i 0.0304398 + 0.0338068i
\(401\) −17.3821 + 7.73903i −0.868023 + 0.386469i −0.791915 0.610631i \(-0.790916\pi\)
−0.0761074 + 0.997100i \(0.524249\pi\)
\(402\) 0 0
\(403\) 1.06635 0.226659i 0.0531185 0.0112907i
\(404\) −0.253650 0.780656i −0.0126196 0.0388391i
\(405\) 0 0
\(406\) −63.3050 −3.14177
\(407\) 5.27538 2.52910i 0.261491 0.125363i
\(408\) 0 0
\(409\) 0.528467 + 5.02803i 0.0261310 + 0.248620i 0.999788 + 0.0206014i \(0.00655810\pi\)
−0.973657 + 0.228019i \(0.926775\pi\)
\(410\) −13.4149 2.85143i −0.662515 0.140822i
\(411\) 0 0
\(412\) 2.99500 28.4955i 0.147553 1.40387i
\(413\) −25.5709 18.5783i −1.25826 0.914180i
\(414\) 0 0
\(415\) −5.50000 16.9273i −0.269984 0.830926i
\(416\) −1.67675 0.746537i −0.0822095 0.0366020i
\(417\) 0 0
\(418\) 13.4482 10.3617i 0.657772 0.506806i
\(419\) 17.6391 30.5518i 0.861727 1.49255i −0.00853378 0.999964i \(-0.502716\pi\)
0.870261 0.492591i \(-0.163950\pi\)
\(420\) 0 0
\(421\) −19.5485 + 21.7108i −0.952736 + 1.05812i 0.0455129 + 0.998964i \(0.485508\pi\)
−0.998249 + 0.0591566i \(0.981159\pi\)
\(422\) −11.9761 + 36.8585i −0.582985 + 1.79424i
\(423\) 0 0
\(424\) 1.97214 + 1.43284i 0.0957754 + 0.0695849i
\(425\) −2.29154 + 0.487082i −0.111156 + 0.0236269i
\(426\) 0 0
\(427\) −5.01514 47.7159i −0.242700 2.30913i
\(428\) 14.3188 24.8009i 0.692125 1.19879i
\(429\) 0 0
\(430\) 6.25329 + 10.8310i 0.301560 + 0.522318i
\(431\) 28.7943 20.9203i 1.38697 1.00770i 0.390785 0.920482i \(-0.372204\pi\)
0.996190 0.0872135i \(-0.0277962\pi\)
\(432\) 0 0
\(433\) −0.819660 + 2.52265i −0.0393904 + 0.121231i −0.968818 0.247773i \(-0.920301\pi\)
0.929428 + 0.369004i \(0.120301\pi\)
\(434\) −4.39423 + 41.8083i −0.210930 + 2.00686i
\(435\) 0 0
\(436\) −24.0141 26.6704i −1.15007 1.27728i
\(437\) 9.28329 + 1.97323i 0.444080 + 0.0943922i
\(438\) 0 0
\(439\) 12.5000 + 21.6506i 0.596592 + 1.03333i 0.993320 + 0.115392i \(0.0368124\pi\)
−0.396728 + 0.917936i \(0.629854\pi\)
\(440\) 0.723944 9.43826i 0.0345127 0.449951i
\(441\) 0 0
\(442\) 2.51722 1.82887i 0.119732 0.0869904i
\(443\) 14.6387 16.2579i 0.695504 0.772436i −0.287149 0.957886i \(-0.592708\pi\)
0.982654 + 0.185450i \(0.0593743\pi\)
\(444\) 0 0
\(445\) −17.4906 + 7.78734i −0.829136 + 0.369155i
\(446\) 6.24356 2.77981i 0.295641 0.131628i
\(447\) 0 0
\(448\) 33.8558 37.6007i 1.59954 1.77647i
\(449\) −23.8323 + 17.3152i −1.12472 + 0.817155i −0.984918 0.173024i \(-0.944646\pi\)
−0.139800 + 0.990180i \(0.544646\pi\)
\(450\) 0 0
\(451\) 5.16312 + 8.38800i 0.243122 + 0.394975i
\(452\) −23.4219 40.5680i −1.10167 1.90816i
\(453\) 0 0
\(454\) −22.9929 4.88729i −1.07911 0.229372i
\(455\) 1.43794 + 1.59699i 0.0674115 + 0.0748680i
\(456\) 0 0
\(457\) −3.66792 + 34.8979i −0.171578 + 1.63246i 0.482405 + 0.875948i \(0.339763\pi\)
−0.653984 + 0.756509i \(0.726903\pi\)
\(458\) −12.2667 + 37.7530i −0.573186 + 1.76408i
\(459\) 0 0
\(460\) 18.1353 13.1760i 0.845561 0.614336i
\(461\) −0.760951 1.31801i −0.0354410 0.0613857i 0.847761 0.530379i \(-0.177950\pi\)
−0.883202 + 0.468993i \(0.844617\pi\)
\(462\) 0 0
\(463\) 10.7812 18.6735i 0.501043 0.867831i −0.498957 0.866627i \(-0.666283\pi\)
0.999999 0.00120439i \(-0.000383369\pi\)
\(464\) 1.73148 + 16.4739i 0.0803817 + 0.764781i
\(465\) 0 0
\(466\) −48.3702 + 10.2814i −2.24071 + 0.476277i
\(467\) −17.1318 12.4470i −0.792766 0.575978i 0.116017 0.993247i \(-0.462987\pi\)
−0.908783 + 0.417269i \(0.862987\pi\)
\(468\) 0 0
\(469\) 3.73607 11.4984i 0.172516 0.530948i
\(470\) −10.7445 + 11.9329i −0.495605 + 0.550425i
\(471\) 0 0
\(472\) 4.95492 8.58216i 0.228068 0.395026i
\(473\) 2.53394 8.61726i 0.116511 0.396222i
\(474\) 0 0
\(475\) 0.831171 + 0.370061i 0.0381367 + 0.0169796i
\(476\) 21.0193 + 64.6908i 0.963419 + 2.96510i
\(477\) 0 0
\(478\) −19.8992 14.4576i −0.910168 0.661275i
\(479\) 3.85144 36.6440i 0.175977 1.67431i −0.448898 0.893583i \(-0.648183\pi\)
0.624875 0.780725i \(-0.285150\pi\)
\(480\) 0 0
\(481\) −0.407308 0.0865761i −0.0185717 0.00394753i
\(482\) −3.14479 29.9206i −0.143241 1.36285i
\(483\) 0 0
\(484\) −22.3084 + 18.2122i −1.01402 + 0.827826i
\(485\) −25.3542 −1.15128
\(486\) 0 0
\(487\) 5.83688 + 17.9641i 0.264494 + 0.814030i 0.991809 + 0.127726i \(0.0407679\pi\)
−0.727315 + 0.686304i \(0.759232\pi\)
\(488\) 14.7140 3.12756i 0.666072 0.141578i
\(489\) 0 0
\(490\) −46.1715 + 20.5569i −2.08582 + 0.928665i
\(491\) −12.9909 14.4279i −0.586273 0.651122i 0.374901 0.927065i \(-0.377677\pi\)
−0.961174 + 0.275943i \(0.911010\pi\)
\(492\) 0 0
\(493\) −38.9650 17.3483i −1.75489 0.781329i
\(494\) −1.20837 −0.0543673
\(495\) 0 0
\(496\) 11.0000 0.493915
\(497\) −41.5807 18.5129i −1.86515 0.830418i
\(498\) 0 0
\(499\) 21.9091 + 24.3325i 0.980786 + 1.08927i 0.995997 + 0.0893892i \(0.0284915\pi\)
−0.0152105 + 0.999884i \(0.504842\pi\)
\(500\) 27.6615 12.3157i 1.23706 0.550774i
\(501\) 0 0
\(502\) 47.7112 10.1413i 2.12945 0.452630i
\(503\) 1.83543 + 5.64888i 0.0818379 + 0.251871i 0.983601 0.180360i \(-0.0577264\pi\)
−0.901763 + 0.432231i \(0.857726\pi\)
\(504\) 0 0
\(505\) 0.673762 0.0299820
\(506\) −27.9327 5.11964i −1.24176 0.227596i
\(507\) 0 0
\(508\) 0.756375 + 7.19643i 0.0335587 + 0.319290i
\(509\) −16.0131 3.40369i −0.709769 0.150866i −0.161139 0.986932i \(-0.551517\pi\)
−0.548629 + 0.836066i \(0.684850\pi\)
\(510\) 0 0
\(511\) 1.09464 10.4148i 0.0484239 0.460722i
\(512\) −20.1016 14.6047i −0.888374 0.645441i
\(513\) 0 0
\(514\) −8.22542 25.3153i −0.362808 1.11661i
\(515\) 21.4855 + 9.56596i 0.946765 + 0.421527i
\(516\) 0 0
\(517\) 11.5276 0.324779i 0.506985 0.0142838i
\(518\) 8.02866 13.9061i 0.352759 0.610997i
\(519\) 0 0
\(520\) −0.450835 + 0.500703i −0.0197704 + 0.0219573i
\(521\) −8.28232 + 25.4903i −0.362855 + 1.11675i 0.588459 + 0.808527i \(0.299735\pi\)
−0.951313 + 0.308225i \(0.900265\pi\)
\(522\) 0 0
\(523\) 30.2984 + 22.0131i 1.32486 + 0.962564i 0.999858 + 0.0168489i \(0.00536341\pi\)
0.324997 + 0.945715i \(0.394637\pi\)
\(524\) −6.30600 + 1.34038i −0.275479 + 0.0585549i
\(525\) 0 0
\(526\) 1.44815 + 13.7782i 0.0631423 + 0.600758i
\(527\) −14.1620 + 24.5293i −0.616907 + 1.06851i
\(528\) 0 0
\(529\) 3.56231 + 6.17009i 0.154883 + 0.268265i
\(530\) −6.85730 + 4.98212i −0.297862 + 0.216409i
\(531\) 0 0
\(532\) 8.16312 25.1235i 0.353916 1.08924i
\(533\) 0.0732820 0.697232i 0.00317420 0.0302005i
\(534\) 0 0
\(535\) 15.7290 + 17.4688i 0.680023 + 0.755242i
\(536\) 3.70779 + 0.788114i 0.160152 + 0.0340414i
\(537\) 0 0
\(538\) −21.7426 37.6594i −0.937392 1.62361i
\(539\) 33.5625 + 13.8240i 1.44564 + 0.595442i
\(540\) 0 0
\(541\) −31.2533 + 22.7068i −1.34368 + 0.976243i −0.344384 + 0.938829i \(0.611912\pi\)
−0.999300 + 0.0374146i \(0.988088\pi\)
\(542\) −1.38841 + 1.54199i −0.0596373 + 0.0662340i
\(543\) 0 0
\(544\) 43.5642 19.3960i 1.86780 0.831597i
\(545\) 26.9116 11.9818i 1.15277 0.513244i
\(546\) 0 0
\(547\) 13.4057 14.8885i 0.573185 0.636586i −0.384939 0.922942i \(-0.625777\pi\)
0.958123 + 0.286356i \(0.0924441\pi\)
\(548\) −0.664066 + 0.482472i −0.0283675 + 0.0206102i
\(549\) 0 0
\(550\) −2.51722 1.03681i −0.107335 0.0442099i
\(551\) 8.28232 + 14.3454i 0.352838 + 0.611134i
\(552\) 0 0
\(553\) −39.2478 8.34238i −1.66899 0.354754i
\(554\) 27.8700 + 30.9528i 1.18408 + 1.31506i
\(555\) 0 0
\(556\) 3.11478 29.6351i 0.132096 1.25681i
\(557\) 1.67867 5.16641i 0.0711274 0.218908i −0.909173 0.416418i \(-0.863285\pi\)
0.980301 + 0.197510i \(0.0632855\pi\)
\(558\) 0 0
\(559\) −0.517221 + 0.375783i −0.0218761 + 0.0158939i
\(560\) 10.8417 + 18.7784i 0.458145 + 0.793531i
\(561\) 0 0
\(562\) 17.7984 30.8277i 0.750779 1.30039i
\(563\) −1.63316 15.5385i −0.0688294 0.654868i −0.973489 0.228733i \(-0.926542\pi\)
0.904660 0.426135i \(-0.140125\pi\)
\(564\) 0 0
\(565\) 37.6106 7.99438i 1.58229 0.336326i
\(566\) 19.0271 + 13.8240i 0.799770 + 0.581067i
\(567\) 0 0
\(568\) 4.40983 13.5721i 0.185032 0.569471i
\(569\) 21.2296 23.5778i 0.889990 0.988435i −0.109994 0.993932i \(-0.535083\pi\)
0.999985 + 0.00549764i \(0.00174996\pi\)
\(570\) 0 0
\(571\) −5.98936 + 10.3739i −0.250647 + 0.434133i −0.963704 0.266973i \(-0.913977\pi\)
0.713057 + 0.701106i \(0.247310\pi\)
\(572\) 2.04897 0.0577277i 0.0856719 0.00241372i
\(573\) 0 0
\(574\) 24.6972 + 10.9959i 1.03084 + 0.458960i
\(575\) −0.470294 1.44742i −0.0196126 0.0603614i
\(576\) 0 0
\(577\) 1.09017 + 0.792055i 0.0453844 + 0.0329737i 0.610246 0.792212i \(-0.291071\pi\)
−0.564862 + 0.825186i \(0.691071\pi\)
\(578\) −4.63138 + 44.0646i −0.192640 + 1.83285i
\(579\) 0 0
\(580\) 38.2696 + 8.13446i 1.58906 + 0.337765i
\(581\) 3.66732 + 34.8923i 0.152146 + 1.44757i
\(582\) 0 0
\(583\) 5.98770 + 1.09745i 0.247985 + 0.0454519i
\(584\) 3.28332 0.135865
\(585\) 0 0
\(586\) −3.31966 10.2169i −0.137134 0.422055i
\(587\) −35.9236 + 7.63579i −1.48272 + 0.315163i −0.876992 0.480506i \(-0.840453\pi\)
−0.605732 + 0.795668i \(0.707120\pi\)
\(588\) 0 0
\(589\) 10.0490 4.47410i 0.414062 0.184352i
\(590\) 23.0565 + 25.6068i 0.949221 + 1.05422i
\(591\) 0 0
\(592\) −3.83838 1.70896i −0.157756 0.0702376i
\(593\) 27.3094 1.12146 0.560732 0.827997i \(-0.310520\pi\)
0.560732 + 0.827997i \(0.310520\pi\)
\(594\) 0 0
\(595\) −55.8328 −2.28892
\(596\) −11.0292 4.91051i −0.451773 0.201142i
\(597\) 0 0
\(598\) 1.35250 + 1.50211i 0.0553080 + 0.0614258i
\(599\) 15.7054 6.99249i 0.641705 0.285705i −0.0599728 0.998200i \(-0.519101\pi\)
0.701678 + 0.712495i \(0.252435\pi\)
\(600\) 0 0
\(601\) 9.15613 1.94619i 0.373486 0.0793869i −0.0173444 0.999850i \(-0.505521\pi\)
0.390831 + 0.920463i \(0.372188\pi\)
\(602\) −7.61825 23.4466i −0.310497 0.955611i
\(603\) 0 0
\(604\) −34.6525 −1.40999
\(605\) −8.55892 22.0347i −0.347970 0.895837i
\(606\) 0 0
\(607\) 2.99140 + 28.4613i 0.121417 + 1.15521i 0.870306 + 0.492511i \(0.163921\pi\)
−0.748889 + 0.662696i \(0.769412\pi\)
\(608\) −18.1151 3.85049i −0.734665 0.156158i
\(609\) 0 0
\(610\) −5.46736 + 52.0184i −0.221367 + 2.10616i
\(611\) −0.664066 0.482472i −0.0268652 0.0195187i
\(612\) 0 0
\(613\) 7.74265 + 23.8294i 0.312723 + 0.962461i 0.976682 + 0.214692i \(0.0688748\pi\)
−0.663959 + 0.747769i \(0.731125\pi\)
\(614\) 33.9050 + 15.0955i 1.36829 + 0.609204i
\(615\) 0 0
\(616\) −5.26403 + 17.9016i −0.212094 + 0.721276i
\(617\) −8.43908 + 14.6169i −0.339745 + 0.588455i −0.984385 0.176031i \(-0.943674\pi\)
0.644640 + 0.764486i \(0.277007\pi\)
\(618\) 0 0
\(619\) 4.60934 5.11919i 0.185265 0.205757i −0.643357 0.765566i \(-0.722459\pi\)
0.828622 + 0.559809i \(0.189125\pi\)
\(620\) 8.02866 24.7097i 0.322439 0.992365i
\(621\) 0 0
\(622\) 49.9959 + 36.3242i 2.00465 + 1.45647i
\(623\) 36.9160 7.84674i 1.47901 0.314373i
\(624\) 0 0
\(625\) 2.39833 + 22.8186i 0.0959332 + 0.912743i
\(626\) −34.0100 + 58.9070i −1.35931 + 2.35440i
\(627\) 0 0
\(628\) 27.0344 + 46.8250i 1.07879 + 1.86852i
\(629\) 8.75261 6.35914i 0.348989 0.253556i
\(630\) 0 0
\(631\) −5.37132 + 16.5312i −0.213829 + 0.658098i 0.785406 + 0.618981i \(0.212454\pi\)
−0.999235 + 0.0391166i \(0.987546\pi\)
\(632\) 1.31499 12.5113i 0.0523076 0.497674i
\(633\) 0 0
\(634\) −0.450835 0.500703i −0.0179049 0.0198854i
\(635\) −5.80979 1.23491i −0.230554 0.0490059i
\(636\) 0 0
\(637\) −1.29180 2.23746i −0.0511828 0.0886513i
\(638\) −25.9813 42.2092i −1.02861 1.67108i
\(639\) 0 0
\(640\) −17.5902 + 12.7800i −0.695313 + 0.505174i
\(641\) −14.2992 + 15.8809i −0.564785 + 0.627258i −0.956115 0.292993i \(-0.905349\pi\)
0.391329 + 0.920251i \(0.372015\pi\)
\(642\) 0 0
\(643\) −37.6007 + 16.7409i −1.48283 + 0.660196i −0.979047 0.203636i \(-0.934724\pi\)
−0.503779 + 0.863833i \(0.668057\pi\)
\(644\) −40.3674 + 17.9727i −1.59070 + 0.708224i
\(645\) 0 0
\(646\) 21.0074 23.3311i 0.826527 0.917951i
\(647\) 9.45368 6.86850i 0.371663 0.270029i −0.386237 0.922399i \(-0.626225\pi\)
0.757900 + 0.652371i \(0.226225\pi\)
\(648\) 0 0
\(649\) 1.89261 24.6745i 0.0742914 0.968558i
\(650\) 0.0968859 + 0.167811i 0.00380018 + 0.00658210i
\(651\) 0 0
\(652\) −3.53897 0.752232i −0.138597 0.0294597i
\(653\) −22.8773 25.4078i −0.895258 0.994285i 0.104742 0.994499i \(-0.466598\pi\)
−1.00000 0.000214284i \(0.999932\pi\)
\(654\) 0 0
\(655\) 0.553143 5.26281i 0.0216131 0.205635i
\(656\) 2.18597 6.72772i 0.0853477 0.262673i
\(657\) 0 0
\(658\) 25.6074 18.6049i 0.998280 0.725293i
\(659\) 16.8782 + 29.2338i 0.657480 + 1.13879i 0.981266 + 0.192658i \(0.0617108\pi\)
−0.323786 + 0.946130i \(0.604956\pi\)
\(660\) 0 0
\(661\) −1.21885 + 2.11111i −0.0474077 + 0.0821125i −0.888755 0.458382i \(-0.848429\pi\)
0.841348 + 0.540494i \(0.181763\pi\)
\(662\) −1.63794 15.5839i −0.0636603 0.605687i
\(663\) 0 0
\(664\) −10.7596 + 2.28703i −0.417554 + 0.0887539i
\(665\) 17.5422 + 12.7452i 0.680258 + 0.494237i
\(666\) 0 0
\(667\) 8.56231 26.3521i 0.331534 1.02036i
\(668\) −18.8228 + 20.9049i −0.728277 + 0.808833i
\(669\) 0 0
\(670\) −6.59017 + 11.4145i −0.254600 + 0.440981i
\(671\) 29.7567 22.9272i 1.14875 0.885095i
\(672\) 0 0
\(673\) 16.6595 + 7.41728i 0.642176 + 0.285915i 0.701874 0.712301i \(-0.252347\pi\)
−0.0596980 + 0.998216i \(0.519014\pi\)
\(674\) −17.6990 54.4719i −0.681740 2.09818i
\(675\) 0 0
\(676\) 27.4164 + 19.9192i 1.05448 + 0.766123i
\(677\) 0.898510 8.54876i 0.0345326 0.328555i −0.963594 0.267370i \(-0.913845\pi\)
0.998126 0.0611851i \(-0.0194880\pi\)
\(678\) 0 0
\(679\) 48.8866 + 10.3912i 1.87609 + 0.398776i
\(680\) −1.82979 17.4093i −0.0701694 0.667617i
\(681\) 0 0
\(682\) −29.6796 + 14.2289i −1.13649 + 0.544852i
\(683\) −0.940588 −0.0359906 −0.0179953 0.999838i \(-0.505728\pi\)
−0.0179953 + 0.999838i \(0.505728\pi\)
\(684\) 0 0
\(685\) −0.208204 0.640786i −0.00795506 0.0244832i
\(686\) 35.1207 7.46513i 1.34091 0.285020i
\(687\) 0 0
\(688\) −5.89314 + 2.62380i −0.224674 + 0.100031i
\(689\) −0.289925 0.321995i −0.0110453 0.0122670i
\(690\) 0 0
\(691\) 29.5630 + 13.1623i 1.12463 + 0.500717i 0.882869 0.469620i \(-0.155609\pi\)
0.241759 + 0.970336i \(0.422276\pi\)
\(692\) −35.0845 −1.33371
\(693\) 0 0
\(694\) 54.0689 2.05243
\(695\) 22.3448 + 9.94854i 0.847586 + 0.377369i
\(696\) 0 0
\(697\) 12.1881 + 13.5362i 0.461656 + 0.512721i
\(698\) 18.0226 8.02418i 0.682166 0.303720i
\(699\) 0 0
\(700\) −4.14350 + 0.880728i −0.156610 + 0.0332884i
\(701\) 7.23071 + 22.2538i 0.273100 + 0.840515i 0.989716 + 0.143047i \(0.0456901\pi\)
−0.716616 + 0.697468i \(0.754310\pi\)
\(702\) 0 0
\(703\) −4.20163 −0.158467
\(704\) 38.9656 + 7.14181i 1.46857 + 0.269167i
\(705\) 0 0
\(706\) 7.58260 + 72.1436i 0.285375 + 2.71516i
\(707\) −1.29911 0.276134i −0.0488580 0.0103851i
\(708\) 0 0
\(709\) 1.58900 15.1184i 0.0596762 0.567782i −0.923304 0.384070i \(-0.874522\pi\)
0.982980 0.183712i \(-0.0588112\pi\)
\(710\) 40.1433 + 29.1658i 1.50655 + 1.09457i
\(711\) 0 0
\(712\) 3.65654 + 11.2537i 0.137035 + 0.421749i
\(713\) −16.8093 7.48398i −0.629513 0.280277i
\(714\) 0 0
\(715\) −0.474658 + 1.61419i −0.0177512 + 0.0603671i
\(716\) −2.55938 + 4.43297i −0.0956484 + 0.165668i
\(717\) 0 0
\(718\) 2.91786 3.24062i 0.108894 0.120939i
\(719\) −4.00726 + 12.3331i −0.149446 + 0.459947i −0.997556 0.0698732i \(-0.977741\pi\)
0.848110 + 0.529820i \(0.177741\pi\)
\(720\) 0 0
\(721\) −37.5066 27.2501i −1.39682 1.01485i
\(722\) 28.0118 5.95409i 1.04249 0.221588i
\(723\) 0 0
\(724\) −3.34851 31.8590i −0.124446 1.18403i
\(725\) 1.32813 2.30039i 0.0493255 0.0854344i
\(726\) 0 0
\(727\) −9.78115 16.9415i −0.362763 0.628324i 0.625652 0.780103i \(-0.284833\pi\)
−0.988414 + 0.151779i \(0.951500\pi\)
\(728\) 1.07448 0.780656i 0.0398229 0.0289330i
\(729\) 0 0
\(730\) −3.52786 + 10.8576i −0.130572 + 0.401860i
\(731\) 1.73626 16.5194i 0.0642178 0.610991i
\(732\) 0 0
\(733\) −9.80442 10.8889i −0.362135 0.402191i 0.534352 0.845262i \(-0.320556\pi\)
−0.896487 + 0.443071i \(0.853889\pi\)
\(734\) −48.4184 10.2917i −1.78716 0.379872i
\(735\) 0 0
\(736\) 15.4894 + 26.8284i 0.570945 + 0.988906i
\(737\) 9.20003 2.22807i 0.338888 0.0820721i
\(738\) 0 0
\(739\) −14.7533 + 10.7189i −0.542709 + 0.394301i −0.825090 0.565001i \(-0.808876\pi\)
0.282381 + 0.959302i \(0.408876\pi\)
\(740\) −6.64044 + 7.37495i −0.244107 + 0.271109i
\(741\) 0 0
\(742\) 15.2637 6.79584i 0.560348 0.249483i
\(743\) 16.5647 7.37506i 0.607698 0.270565i −0.0797305 0.996816i \(-0.525406\pi\)
0.687429 + 0.726252i \(0.258739\pi\)
\(744\) 0 0
\(745\) 6.63097 7.36444i 0.242940 0.269812i
\(746\) 25.0636 18.2098i 0.917643 0.666707i
\(747\) 0 0
\(748\) −34.5066 + 40.5649i −1.26169 + 1.48320i
\(749\) −23.1683 40.1286i −0.846550 1.46627i
\(750\) 0 0
\(751\) 1.47366 + 0.313235i 0.0537745 + 0.0114301i 0.234720 0.972063i \(-0.424583\pi\)
−0.180946 + 0.983493i \(0.557916\pi\)
\(752\) −5.54195 6.15496i −0.202094 0.224448i
\(753\) 0 0
\(754\) −0.368762 + 3.50854i −0.0134295 + 0.127773i
\(755\) 8.78962 27.0517i 0.319887 0.984511i
\(756\) 0 0
\(757\) 33.0795 24.0337i 1.20230 0.873519i 0.207787 0.978174i \(-0.433374\pi\)
0.994509 + 0.104655i \(0.0333738\pi\)
\(758\) −6.70053 11.6057i −0.243374 0.421537i
\(759\) 0 0
\(760\) −3.39919 + 5.88756i −0.123301 + 0.213564i
\(761\) −3.49572 33.2596i −0.126720 1.20566i −0.854353 0.519693i \(-0.826046\pi\)
0.727633 0.685966i \(-0.240620\pi\)
\(762\) 0 0
\(763\) −56.7999 + 12.0732i −2.05630 + 0.437079i
\(764\) 21.0193 + 15.2714i 0.760452 + 0.552501i
\(765\) 0 0
\(766\) −22.6246 + 69.6314i −0.817460 + 2.51588i
\(767\) −1.17862 + 1.30899i −0.0425574 + 0.0472648i
\(768\) 0 0
\(769\) 11.1353 19.2868i 0.401548 0.695501i −0.592365 0.805669i \(-0.701806\pi\)
0.993913 + 0.110169i \(0.0351391\pi\)
\(770\) −53.5429 36.6426i −1.92955 1.32051i
\(771\) 0 0
\(772\) 17.6554 + 7.86069i 0.635432 + 0.282912i
\(773\) −10.4084 32.0338i −0.374364 1.15217i −0.943907 0.330213i \(-0.892879\pi\)
0.569542 0.821962i \(-0.307121\pi\)
\(774\) 0 0
\(775\) −1.42705 1.03681i −0.0512612 0.0372434i
\(776\) −1.63794 + 15.5839i −0.0587986 + 0.559431i
\(777\) 0 0
\(778\) −46.8966 9.96817i −1.68132 0.357376i
\(779\) −0.739428 7.03519i −0.0264928 0.252062i
\(780\) 0 0
\(781\) −4.72167 35.3223i −0.168955 1.26393i
\(782\) −52.5157 −1.87796
\(783\) 0 0
\(784\) −8.05573 24.7930i −0.287705 0.885464i
\(785\) −43.4115 + 9.22741i −1.54942 + 0.329340i
\(786\) 0 0
\(787\) 25.3756 11.2980i 0.904544 0.402729i 0.0988781 0.995100i \(-0.468475\pi\)
0.805665 + 0.592371i \(0.201808\pi\)
\(788\) −4.31381 4.79097i −0.153673 0.170671i
\(789\) 0 0
\(790\) 39.9609 + 17.7917i 1.42174 + 0.633002i
\(791\) −75.7950 −2.69496
\(792\) 0 0
\(793\) −2.67376 −0.0949481
\(794\) 47.9336 + 21.3414i 1.70110 + 0.757379i
\(795\) 0 0
\(796\) 0.729466 + 0.810154i 0.0258552 + 0.0287152i
\(797\) 3.92635 1.74812i 0.139078 0.0619217i −0.336017 0.941856i \(-0.609080\pi\)
0.475096 + 0.879934i \(0.342413\pi\)
\(798\) 0 0
\(799\) 20.8602 4.43397i 0.737981 0.156863i
\(800\) 0.917716 + 2.82444i 0.0324462 + 0.0998590i
\(801\) 0 0
\(802\) −40.8885 −1.44382
\(803\) 7.39340 3.54452i 0.260908 0.125083i
\(804\) 0 0
\(805\) −3.79130 36.0718i −0.133626 1.27136i
\(806\) 2.29154 + 0.487082i 0.0807160 + 0.0171567i
\(807\) 0 0
\(808\) 0.0435265 0.414127i 0.00153126 0.0145689i
\(809\) 5.72294 + 4.15796i 0.201208 + 0.146186i 0.683827 0.729644i \(-0.260314\pi\)
−0.482619 + 0.875830i \(0.660314\pi\)
\(810\) 0 0
\(811\) −13.6631 42.0508i −0.479777 1.47660i −0.839405 0.543506i \(-0.817096\pi\)
0.359628 0.933096i \(-0.382904\pi\)
\(812\) −70.4554 31.3688i −2.47250 1.10083i
\(813\) 0 0
\(814\) 12.5671 0.354065i 0.440476 0.0124100i
\(815\) 1.48490 2.57191i 0.0520136 0.0900902i
\(816\) 0 0
\(817\) −4.31646 + 4.79392i −0.151014 + 0.167718i
\(818\) −3.35733 + 10.3328i −0.117386 + 0.361278i
\(819\) 0 0
\(820\) −13.5172 9.82084i −0.472042 0.342958i
\(821\) −38.9008 + 8.26863i −1.35765 + 0.288577i −0.828518 0.559963i \(-0.810815\pi\)
−0.529131 + 0.848540i \(0.677482\pi\)
\(822\) 0 0
\(823\) −1.99769 19.0068i −0.0696351 0.662534i −0.972547 0.232708i \(-0.925241\pi\)
0.902912 0.429826i \(-0.141425\pi\)
\(824\) 7.26771 12.5880i 0.253183 0.438525i
\(825\) 0 0
\(826\) −33.9615 58.8230i −1.18167 2.04672i
\(827\) −9.41667 + 6.84161i −0.327450 + 0.237906i −0.739348 0.673324i \(-0.764866\pi\)
0.411898 + 0.911230i \(0.364866\pi\)
\(828\) 0 0
\(829\) 6.19098 19.0539i 0.215022 0.661769i −0.784130 0.620596i \(-0.786891\pi\)
0.999152 0.0411726i \(-0.0131094\pi\)
\(830\) 3.99801 38.0385i 0.138773 1.32034i
\(831\) 0 0
\(832\) −1.88672 2.09542i −0.0654103 0.0726455i
\(833\) 65.6583 + 13.9561i 2.27492 + 0.483550i
\(834\) 0 0
\(835\) −11.5451 19.9967i −0.399534 0.692013i
\(836\) 20.1016 4.86822i 0.695228 0.168371i
\(837\) 0 0
\(838\) 61.3328 44.5609i 2.11871 1.53933i
\(839\) −9.35604 + 10.3909i −0.323006 + 0.358735i −0.882677 0.469980i \(-0.844261\pi\)
0.559671 + 0.828715i \(0.310928\pi\)
\(840\) 0 0
\(841\) 17.6869 7.87470i 0.609892 0.271541i
\(842\) −57.3537 + 25.5355i −1.97654 + 0.880012i
\(843\) 0 0
\(844\) −31.5929 + 35.0874i −1.08747 + 1.20776i
\(845\) −22.5042 + 16.3503i −0.774168 + 0.562466i
\(846\) 0 0
\(847\) 7.47214 + 45.9937i 0.256746 + 1.58036i
\(848\) −2.18597 3.78621i −0.0750665 0.130019i
\(849\) 0 0
\(850\) −4.92443 1.04672i −0.168906 0.0359022i
\(851\) 4.70278 + 5.22297i 0.161209 + 0.179041i
\(852\) 0 0
\(853\) 0.123379 1.17387i 0.00422442 0.0401927i −0.992207 0.124603i \(-0.960234\pi\)
0.996431 + 0.0844108i \(0.0269008\pi\)
\(854\) 31.8610 98.0581i 1.09026 3.35548i
\(855\) 0 0
\(856\) 11.7533 8.53926i 0.401719 0.291866i
\(857\) −6.91718 11.9809i −0.236286 0.409260i 0.723359 0.690472i \(-0.242597\pi\)
−0.959646 + 0.281212i \(0.909264\pi\)
\(858\) 0 0
\(859\) −21.2082 + 36.7337i −0.723615 + 1.25334i 0.235927 + 0.971771i \(0.424187\pi\)
−0.959542 + 0.281566i \(0.909146\pi\)
\(860\) 1.59265 + 15.1530i 0.0543088 + 0.516714i
\(861\) 0 0
\(862\) 74.8139 15.9022i 2.54817 0.541631i
\(863\) 27.8167 + 20.2100i 0.946893 + 0.687958i 0.950070 0.312037i \(-0.101011\pi\)
−0.00317717 + 0.999995i \(0.501011\pi\)
\(864\) 0 0
\(865\) 8.89919 27.3889i 0.302581 0.931250i
\(866\) −3.81409 + 4.23598i −0.129608 + 0.143944i
\(867\) 0 0
\(868\) −25.6074 + 44.3533i −0.869171 + 1.50545i
\(869\) −10.5455 29.5927i −0.357732 1.00386i
\(870\) 0 0
\(871\) −0.615512 0.274044i −0.0208558 0.00928562i
\(872\) −5.62605 17.3152i −0.190522 0.586367i
\(873\) 0 0
\(874\) 16.5000 + 11.9880i 0.558121 + 0.405499i
\(875\) 5.12114 48.7244i 0.173126 1.64719i
\(876\) 0 0
\(877\) −11.2214 2.38519i −0.378921 0.0805422i 0.0145137 0.999895i \(-0.495380\pi\)
−0.393435 + 0.919352i \(0.628713\pi\)
\(878\) 5.61569 + 53.4297i 0.189520 + 1.80317i
\(879\) 0 0
\(880\) −8.07106 + 14.9357i −0.272075 + 0.503483i
\(881\) 34.3376 1.15686 0.578432 0.815730i \(-0.303665\pi\)
0.578432 + 0.815730i \(0.303665\pi\)
\(882\) 0 0
\(883\) −4.36068 13.4208i −0.146749 0.451646i 0.850483 0.526002i \(-0.176310\pi\)
−0.997232 + 0.0743567i \(0.976310\pi\)
\(884\) 3.70779 0.788114i 0.124706 0.0265072i
\(885\) 0 0
\(886\) 42.9487 19.1220i 1.44289 0.642415i
\(887\) −37.8554 42.0427i −1.27106 1.41166i −0.868062 0.496456i \(-0.834634\pi\)
−0.402999 0.915200i \(-0.632032\pi\)
\(888\) 0 0
\(889\) 10.6960 + 4.76216i 0.358732 + 0.159718i
\(890\) −41.1438 −1.37914
\(891\) 0 0
\(892\) 8.32624 0.278783
\(893\) −7.56627 3.36872i −0.253196 0.112730i
\(894\) 0 0
\(895\) −2.81144 3.12242i −0.0939760 0.104371i
\(896\) 39.1541 17.4325i 1.30805 0.582379i
\(897\) 0 0
\(898\) −61.9216 + 13.1618i −2.06635 + 0.439216i
\(899\) −9.92398 30.5429i −0.330983 1.01866i
\(900\) 0 0
\(901\) 11.2574 0.375037
\(902\) 2.80448 + 20.9800i 0.0933789 + 0.698557i
\(903\) 0 0
\(904\) −2.48401 23.6338i −0.0826169 0.786047i
\(905\) 25.7202 + 5.46700i 0.854969 + 0.181729i
\(906\) 0 0
\(907\) 3.74915 35.6708i 0.124488 1.18443i −0.736728 0.676190i \(-0.763630\pi\)
0.861216 0.508239i \(-0.169703\pi\)
\(908\) −23.1683 16.8327i −0.768866 0.558614i
\(909\) 0 0
\(910\) 1.42705 + 4.39201i 0.0473063 + 0.145594i
\(911\) 8.71196 + 3.87882i 0.288640 + 0.128511i 0.545949 0.837818i \(-0.316169\pi\)
−0.257309 + 0.966329i \(0.582836\pi\)
\(912\) 0 0
\(913\) −21.7596 + 16.7655i −0.720138 + 0.554858i
\(914\) −37.7037 + 65.3047i −1.24713 + 2.16009i
\(915\) 0 0
\(916\) −32.3596 + 35.9390i −1.06919 + 1.18746i
\(917\) −3.22344 + 9.92073i −0.106447 + 0.327611i
\(918\) 0 0
\(919\) 20.3713 + 14.8006i 0.671988 + 0.488228i 0.870690 0.491832i \(-0.163673\pi\)
−0.198702 + 0.980060i \(0.563673\pi\)
\(920\) 11.1234 2.36434i 0.366726 0.0779501i
\(921\) 0 0
\(922\) −0.341861 3.25259i −0.0112586 0.107118i
\(923\) −1.26825 + 2.19668i −0.0417450 + 0.0723045i
\(924\) 0 0
\(925\) 0.336881 + 0.583495i 0.0110766 + 0.0191852i
\(926\) 37.4871 27.2359i 1.23190 0.895029i
\(927\) 0 0
\(928\) −16.7082 + 51.4226i −0.548474 + 1.68803i
\(929\) −4.39423 + 41.8083i −0.144170 + 1.37169i 0.648118 + 0.761540i \(0.275556\pi\)
−0.792288 + 0.610147i \(0.791110\pi\)
\(930\) 0 0
\(931\) −17.4435 19.3730i −0.571687 0.634923i
\(932\) −58.9284 12.5256i −1.93026 0.410290i
\(933\) 0 0
\(934\) −22.7533 39.4099i −0.744510 1.28953i
\(935\) −22.9146 37.2271i −0.749388 1.21746i
\(936\) 0 0
\(937\) −8.75329 + 6.35964i −0.285957 + 0.207760i −0.721512 0.692402i \(-0.756552\pi\)
0.435554 + 0.900162i \(0.356552\pi\)
\(938\) 17.3849 19.3079i 0.567637 0.630424i
\(939\) 0 0
\(940\) −17.8711 + 7.95671i −0.582890 + 0.259519i
\(941\) −8.38375 + 3.73269i −0.273303 + 0.121682i −0.538812 0.842426i \(-0.681127\pi\)
0.265509 + 0.964108i \(0.414460\pi\)
\(942\) 0 0
\(943\) −7.91770 + 8.79350i −0.257836 + 0.286356i
\(944\) −14.3787 + 10.4467i −0.467986 + 0.340011i
\(945\) 0 0
\(946\) 12.5066 14.7024i 0.406624 0.478015i
\(947\) 11.1922 + 19.3855i 0.363699 + 0.629944i 0.988566 0.150786i \(-0.0481805\pi\)
−0.624868 + 0.780731i \(0.714847\pi\)
\(948\) 0 0
\(949\) −0.570839 0.121336i −0.0185302 0.00393872i
\(950\) 1.30828 + 1.45299i 0.0424461 + 0.0471412i
\(951\) 0 0
\(952\) −3.60692 + 34.3175i −0.116901 + 1.11224i
\(953\) 5.19277 15.9817i 0.168210 0.517698i −0.831048 0.556200i \(-0.812259\pi\)
0.999259 + 0.0385025i \(0.0122587\pi\)
\(954\) 0 0
\(955\) −17.2533 + 12.5352i −0.558303 + 0.405631i
\(956\) −14.9828 25.9511i −0.484580 0.839317i
\(957\) 0 0
\(958\) 39.5902 68.5722i 1.27910 2.21547i
\(959\) 0.138827 + 1.32086i 0.00448297 + 0.0426526i
\(960\) 0 0
\(961\) 9.46237 2.01129i 0.305238 0.0648803i
\(962\) −0.723944 0.525976i −0.0233409 0.0169582i
\(963\) 0 0
\(964\) 11.3262 34.8586i 0.364794 1.12272i
\(965\) −10.6148 + 11.7889i −0.341702 + 0.379499i
\(966\) 0 0
\(967\) 8.84346 15.3173i 0.284386 0.492572i −0.688074 0.725641i \(-0.741543\pi\)
0.972460 + 0.233069i \(0.0748768\pi\)
\(968\) −14.0965 + 3.83724i −0.453079 + 0.123334i
\(969\) 0 0
\(970\) −49.7748 22.1612i −1.59817 0.711552i
\(971\) 0.313529 + 0.964944i 0.0100616 + 0.0309665i 0.955961 0.293493i \(-0.0948177\pi\)
−0.945900 + 0.324459i \(0.894818\pi\)
\(972\) 0 0
\(973\) −39.0066 28.3399i −1.25049 0.908537i
\(974\) −4.24289 + 40.3684i −0.135951 + 1.29349i
\(975\) 0 0
\(976\) −26.3892 5.60919i −0.844697 0.179546i
\(977\) 0.350937 + 3.33894i 0.0112275 + 0.106822i 0.998700 0.0509665i \(-0.0162302\pi\)
−0.987473 + 0.157789i \(0.949564\pi\)
\(978\) 0 0
\(979\) 20.3828 + 21.3937i 0.651436 + 0.683745i
\(980\) −61.5731 −1.96688
\(981\) 0 0
\(982\) −12.8926 39.6794i −0.411420 1.26622i
\(983\) 49.6004 10.5429i 1.58201 0.336266i 0.668698 0.743534i \(-0.266852\pi\)
0.913309 + 0.407268i \(0.133519\pi\)
\(984\) 0 0
\(985\) 4.83430 2.15237i 0.154033 0.0685801i
\(986\) −61.3315 68.1155i −1.95319 2.16924i
\(987\) 0 0
\(988\) −1.34486 0.598772i −0.0427858 0.0190495i
\(989\) 10.7905 0.343119
\(990\) 0 0
\(991\) −58.2705 −1.85102 −0.925512 0.378719i \(-0.876365\pi\)
−0.925512 + 0.378719i \(0.876365\pi\)
\(992\) 32.8011 + 14.6040i 1.04144 + 0.463677i
\(993\) 0 0
\(994\) −65.4487 72.6881i −2.07591 2.30553i
\(995\) −0.817481 + 0.363966i −0.0259159 + 0.0115385i
\(996\) 0 0
\(997\) −37.8960 + 8.05505i −1.20018 + 0.255106i −0.764277 0.644888i \(-0.776904\pi\)
−0.435902 + 0.899994i \(0.643571\pi\)
\(998\) 21.7433 + 66.9189i 0.688271 + 2.11828i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 891.2.n.e.190.2 16
3.2 odd 2 inner 891.2.n.e.190.1 16
9.2 odd 6 inner 891.2.n.e.784.2 16
9.4 even 3 99.2.f.c.91.1 yes 8
9.5 odd 6 99.2.f.c.91.2 yes 8
9.7 even 3 inner 891.2.n.e.784.1 16
11.4 even 5 inner 891.2.n.e.433.1 16
33.26 odd 10 inner 891.2.n.e.433.2 16
99.4 even 15 99.2.f.c.37.1 8
99.13 odd 30 1089.2.a.w.1.1 4
99.31 even 15 1089.2.a.v.1.4 4
99.59 odd 30 99.2.f.c.37.2 yes 8
99.68 even 30 1089.2.a.w.1.4 4
99.70 even 15 inner 891.2.n.e.136.2 16
99.86 odd 30 1089.2.a.v.1.1 4
99.92 odd 30 inner 891.2.n.e.136.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.f.c.37.1 8 99.4 even 15
99.2.f.c.37.2 yes 8 99.59 odd 30
99.2.f.c.91.1 yes 8 9.4 even 3
99.2.f.c.91.2 yes 8 9.5 odd 6
891.2.n.e.136.1 16 99.92 odd 30 inner
891.2.n.e.136.2 16 99.70 even 15 inner
891.2.n.e.190.1 16 3.2 odd 2 inner
891.2.n.e.190.2 16 1.1 even 1 trivial
891.2.n.e.433.1 16 11.4 even 5 inner
891.2.n.e.433.2 16 33.26 odd 10 inner
891.2.n.e.784.1 16 9.7 even 3 inner
891.2.n.e.784.2 16 9.2 odd 6 inner
1089.2.a.v.1.1 4 99.86 odd 30
1089.2.a.v.1.4 4 99.31 even 15
1089.2.a.w.1.1 4 99.13 odd 30
1089.2.a.w.1.4 4 99.68 even 30